Problem: Solve the system of equations. $\begin{aligned} & -10x+3y = 5 \\\\ & x=y-4 \end{aligned}$ $ x=$
Solution: We are given that ${x}={y-4}$. Let's substitute this expression into the first equation and solve for $y$ as follows: $ \begin{aligned} -10{x}+3y &= 5\\\\ -10\cdot({y-4})+3y&=5\\\\ -10y+40+3y&=5\\\\ -7y&=-35\\\\ y&=5 \end{aligned}$ Since we now know that ${y}={5}$, we can substitute this value in the second equation to solve for $x$ as follows: $\begin{aligned} x &= {y}-4 \\\\ x&={5}-4\\\\ x&=1 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = 1 \\\\ &y=5 \end{aligned}$